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9y(6y+15)=50
We move all terms to the left:
9y(6y+15)-(50)=0
We multiply parentheses
54y^2+135y-50=0
a = 54; b = 135; c = -50;
Δ = b2-4ac
Δ = 1352-4·54·(-50)
Δ = 29025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29025}=\sqrt{225*129}=\sqrt{225}*\sqrt{129}=15\sqrt{129}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-15\sqrt{129}}{2*54}=\frac{-135-15\sqrt{129}}{108} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+15\sqrt{129}}{2*54}=\frac{-135+15\sqrt{129}}{108} $
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